Problem: Solve for $x$ and $y$ using substitution. ${6x-4y = -8}$ ${y = -2x-5}$
Solution: Since $y$ has already been solved for, substitute $-2x-5$ for $y$ in the first equation. ${6x - 4}{(-2x-5)}{= -8}$ Simplify and solve for $x$ $6x+8x + 20 = -8$ $14x+20 = -8$ $14x+20{-20} = -8{-20}$ $14x = -28$ $\dfrac{14x}{{14}} = \dfrac{-28}{{14}}$ ${x = -2}$ Now that you know ${x = -2}$ , plug it back into $\thinspace {y = -2x-5}\thinspace$ to find $y$ ${y = -2}{(-2)}{ - 5}$ $y = 4 - 5$ $y = -1$ You can also plug ${x = -2}$ into $\thinspace {6x-4y = -8}\thinspace$ and get the same answer for $y$ : ${6}{(-2)}{ - 4y = -8}$ ${y = -1}$